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A collision that conserves momentum but loses kinetic energy

Choose the system before a sticking collision, then check both momentum and kinetic energy.

Question

A 2 kg cart moving right at 3 m/s sticks to a stationary 1 kg cart. External horizontal impulse is negligible. What is their velocity immediately after the collision?

  1. a.1 m/s right
  2. b.2 m/s right
  3. c.3 m/s right
  4. d.About 2.45 m/s right

Correct answer

B. 2 m/s right

Full reasoning

  1. 1Choose both carts together as the system; their contact forces are internal.
  2. 2The initial momentum is (2)(3) + (1)(0) = 6 kg m/s to the right.
  3. 3The combined mass is 3 kg, so the final velocity is 6/3 = 2 m/s to the right.
  4. 4Initial kinetic energy is 9 J; final kinetic energy is 6 J. The 3 J difference becomes other forms of energy. Momentum conservation does not require kinetic energy conservation.

Why each choice is right or wrong

Choice A

This does not preserve the initial total momentum of 6 kg m/s.

Choice B

Correct. The final 3 kg mass carries the initial momentum of 6 kg m/s.

Choice C

This preserves the first cart’s speed but not the two-cart momentum: 3 kg at 3 m/s would carry 9 kg m/s rather than 6.

Choice D

This comes from conserving kinetic energy, which a sticking collision does not conserve.

Related formula

Momentum conservation for two sticking carts

m1 v1 + m2 v2 = (m1 + m2) vf

Assumptions: The carts stick together and the external impulse along the chosen axis is negligible.

Related topic and practice

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Sources

Original authored exercise; no database question ID and no protected or official exam-bank content. Specialist review pending.

  1. University Physics Volume 1, Section 9.3: Conservation of Linear MomentumOpenStax. Accessed 2026-08-02. OpenStax textbook content is CC BY-NC-SA 4.0; attribute and avoid verbatim reuse beyond short cited references.
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Sources and corrections

Sources last checked 2026-09-13

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